The swim force as a body force

Net (as opposed to random) motion of active matter results from an average swim (or propulsive) force. It is shown that the average swim force acts like a body force -- an {\em internal} body force [Yan and Brady, \textit{Soft Matter}, DOI:10.1039/C5SM01318F]. As a result, the particle-pressure exerted on a container wall is the sum of the swim pressure [Takatori \textit{et al., Phys. Rev. Lett.}, 2014, \textbf{113}, 028103] and the `weight' of the active particles. A continuum mechanical description is possible when variations occur on scales larger than the run length of the active particles and gives a Boltzmann-like distribution from a balance of the swim force and the swim pressure. Active particles may also display `action at a distance' and accumulate adjacent to (or be depleted from) a boundary without any external forces. In the momentum balance for the suspension -- the mixture of active particles plus fluid -- only {\textit{external}} body forces appear.